GATE Chemical Engineering Fluid Mechanics and Mechanical Operations Syllabus

Fluid Mechanics and Mechanical Operations syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Fluid Mechanics and Mechanical Operations in GATE Chemical Engineering, not a summary of it.

1. 1

   Fluid Mechanics

   15 topics

   • Fluid Statics
   • Surface Tension
   • Newtonian and Non-Newtonian Fluids
   • Transport Properties
   • Shell-Balances
     • Differential form of Bernoulli Equation
     • Energy Balance
   • Equations
     • Equation of Continuity
     • Equation of Motion
     • Equation of Mechanical Energy
   • Macroscopic Friction Factors
   • Dimensional Analysis and Similitude
   • Flow through Pipeline Systems
   • Velocity Profiles
   • Flow Meters
   • Pumps and Compressors
   • Elementary Boundary Layer Theory
   • Flow past Immersed Bodies
     • Packed and Fluidized Beds
   • Turbulent Flow
     • Fluctuating Velocity
     • Universal Velocity Profile
     • Pressure Drop
2. 2

   Mechanical Operations

   9 topics

   • Particle Size and Shape
   • Particle Size Distribution
   • Size Reduction and Classification of Solid Particles
   • Free and Hindered Settling
   • Centrifuge and Cyclones
   • Thickening and Classification
   • Filtration
   • Agitation and Mixing
   • Conveying of Solids

Fluid Mechanics and Mechanical Operations flashcards for GATE Chemical Engineering

18 of 51 cards from the Fluid Mechanics and Mechanical Operations deck — real questions with worked answers.

1. State the basic equation of fluid statics (hydrostatic pressure variation with depth in a static fluid).

   For a static fluid the pressure varies with depth as $$\frac{dp}{dz} = -\rho g$$ For an incompressible fluid this integrates to $p = p_{0} + \rho g h$, where $h$ is the depth below the surface.

2. What is the magnitude and line of action of the hydrostatic force on a submerged plane surface?

   The resultant force is $F = \rho g \bar{h} A$, where $\bar{h}$ is the depth of the centroid. It acts at the center of pressure, located below the centroid at $y_{cp} = \bar{y} + \frac{I_{\bar{x}}}{\bar{y} A}$.

3. State Pascal's law for a fluid at rest.

   At any point in a fluid at rest, the pressure is the same in all directions (isotropic); it acts equally in every direction and is independent of orientation of the surface.

4. State Archimedes' principle and the buoyant force expression.

   A body immersed in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid: $$F_{B} = \rho_{fluid}\, g\, V_{displaced}$$

5. Define surface tension and give its SI units.

   Surface tension $\sigma$ is the force per unit length acting along a liquid surface (or the surface free energy per unit area) due to unbalanced cohesive forces at the interface. SI units: $\mathrm{N/m}$ (or $\mathrm{J/m^{2}}$).

6. Give the Young-Laplace equation for the pressure difference across a curved interface, and the special cases for a spherical droplet and a soap bubble.

   General: $\Delta p = \sigma\left(\frac{1}{R_{1}} + \frac{1}{R_{2}}\right)$. For a liquid droplet (one surface): $\Delta p = \frac{2\sigma}{R}$. For a soap bubble (two surfaces): $\Delta p = \frac{4\sigma}{R}$.

7. State the capillary rise formula and explain its dependence on tube radius.

   $$h = \frac{2\sigma \cos\theta}{\rho g r}$$ where $\theta$ is the contact angle and $r$ the tube radius. Rise is inversely proportional to $r$; smaller tubes give greater rise. $h<0$ (depression) when $\theta > 90^{\circ}$.

8. Define a Newtonian fluid and state Newton's law of viscosity.

   A Newtonian fluid has shear stress directly proportional to the shear (strain) rate, with constant viscosity: $$\tau = \mu \frac{du}{dy}$$ Examples: water, air, most gases and light oils.

9. Classify non-Newtonian time-independent fluids and give the power-law (Ostwald-de Waele) model.

   Power law: $\tau = K \left(\frac{du}{dy}\right)^{n}$. Pseudoplastic (shear-thinning, $n<1$, e.g. polymer melts, blood); Dilatant (shear-thickening, $n>1$, e.g. starch suspensions); Bingham plastic needs a yield stress: $\tau = \tau_{0} + \mu_{p}\frac{du}{dy}$.

10. Compare thixotropic and rheopectic fluids (time-dependent non-Newtonian behavior).

    Thixotropic: apparent viscosity decreases with time under constant shear (e.g. paints, ketchup). Rheopectic: apparent viscosity increases with time under constant shear (e.g. gypsum suspensions). Both are time-dependent at fixed shear rate.

11. Define the three molecular transport properties and the gradients they relate to.

    Momentum transport: viscosity $\mu$ relates shear stress to velocity gradient (Newton's law). Heat transport: thermal conductivity $k$ relates heat flux to temperature gradient (Fourier's law $q=-k\nabla T$). Mass transport: diffusivity $D_{AB}$ relates molar flux to concentration gradient (Fick's law $J_{A}=-D_{AB}\nabla C_{A}$).

12. Define kinematic viscosity and give its relation to dynamic viscosity and units.

    Kinematic viscosity $\nu = \frac{\mu}{\rho}$, the momentum diffusivity. SI units $\mathrm{m^{2}/s}$ (CGS: stokes, $1\,\mathrm{St}=10^{-4}\,\mathrm{m^{2}/s}$). Dynamic viscosity $\mu$ has units $\mathrm{Pa\cdot s}$ (poise in CGS).

13. What is a shell (momentum) balance and what general form does it take at steady state?

    A shell balance applies conservation of momentum to a thin differential shell of fluid. At steady state: (rate of momentum in) − (rate of momentum out) + (sum of forces) = 0. Letting shell thickness go to zero yields a differential equation for the momentum flux/velocity profile.

14. For steady laminar flow in a horizontal pipe, what is the shear-stress distribution from a shell momentum balance?

    The shear stress varies linearly with radius: $$\tau_{rz} = \left(\frac{p_{0}-p_{L}}{2L}\right) r$$ It is zero at the center ($r=0$) and maximum at the wall ($r=R$).

15. State the differential form of the Bernoulli equation along a streamline for inviscid incompressible flow.

    $$\frac{dp}{\rho} + g\,dz + u\,du = 0$$ Integrating along a streamline gives $\frac{p}{\rho} + gz + \frac{u^{2}}{2} = \text{constant}$.

16. State the macroscopic mechanical energy (engineering Bernoulli) balance with friction and pump work.

    $$\frac{p_{1}}{\rho} + \frac{u_{1}^{2}}{2} + g z_{1} + W_{s} = \frac{p_{2}}{\rho} + \frac{u_{2}^{2}}{2} + g z_{2} + h_{f}$$ where $W_{s}$ is shaft work added per unit mass and $h_{f}$ is the friction loss per unit mass.

17. List the assumptions required for the classic (ideal) Bernoulli equation to apply.

    Steady flow; incompressible fluid; inviscid (frictionless, no viscous losses); flow along a single streamline; no shaft work or heat addition between the two points.

18. State the differential equation of continuity (general and incompressible forms).

    General: $$\frac{\partial \rho}{\partial t} + \nabla\cdot(\rho \vec{v}) = 0$$ For incompressible flow ($\rho$ constant): $\nabla\cdot\vec{v} = 0$, i.e. $\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$.

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